| Summary: | Let τn be a type of algebras in which all operation symbols have arity n, for a fixed n ≥ 1. For 0 < r ≤ n, this paper introduces a special kind of n-ary terms of type τn called K*(n, r)-full terms. The set of all K*(n, r)-full terms of type τn is closed under the superposition operation Sn; hence forms a clone denoted by cloneK*(n,r)(τn). We prove that cloneK* (n,r)(τn) is a Menger algebra of rank n. We study K*(n, r)-full hypersubstitutions and the related K*(n, r)-full closed identities and K*(n, r)-full closed varieties. A connection between identities in cloneK* (n,r)(τn) and K* (n, r)-full closed identities is established. The results obtained generalize the results of Denecke and Jampachon [K. Denecke and P. Jampachon, Clones of full terms, Algebra and Discrete Math. 4 (2004) 1–11].
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